In Exercises 27 to 32, use SSS, SAS, ASA, or AAS to prove that the triangles are congruent. Given: P N ¯ bisects M Q ¯ ∠ M and ∠ Q are right angles Prove: Δ P Q R ≅ Δ N M R
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Elementary Geometry for College St...
6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698
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Elementary Geometry for College St...
6th Edition
Daniel C. Alexander + 1 other
Publisher: Cengage Learning
ISBN: 9781285195698
Solutions
Chapter
Section
Chapter 3.1, Problem 30E
Textbook Problem
In Exercises 27 to 32, use SSS, SAS, ASA, or AAS to prove that the triangles are congruent.
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| Prove: |
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Expert Solution
Chapter 3 Solutions
Elementary Geometry for College Students
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addCh. 3.1 - In Exercises 1 to 4, consider the congruent...Ch. 3.1 - In Exercises 1 to 4. consider the congruent...Ch. 3.1 - In Exercises 1 to 4. consider the congruent...Ch. 3.1 - In Exercises 1 to 4, consider the congruent...Ch. 3.1 - Consider ABC and ABD in the figure shown. By the...Ch. 3.1 - In a right triangle, the sides that form the right...Ch. 3.1 - In ABC, the midpoints of the sides are joined. a...Ch. 3.1 - a. Suppose that you wish to prove that RSTSRV....Ch. 3.1 - In Exercises 9 to 12, congruent parts are...Ch. 3.1 - In Exercises 9 to 12, congruent parts are...
Ch. 3.1 - In Exercises 9 to 12, congruent parts are...Ch. 3.1 - In Exercises 9 to 12, congruent parts are...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 13 to 18, use only the given...Ch. 3.1 - In Exercises 19 and 20, the triangles to be proved...Ch. 3.1 - In Exercises 19 and 20, the triangles to be proved...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 21 to 24, the triangles named can be...Ch. 3.1 - In Exercises 25 and 26, complete each proof. Use...Ch. 3.1 - In Exercises 25 and 26, complete each proof. Use...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 27 to 32, use SSS, SAS, ASA, or AAS...Ch. 3.1 - In Exercises 33 to 36, the methods to be used are...Ch. 3.1 - In Exercises 33 to 36, the methods to be used are...Ch. 3.1 - In Exercises 33 to 36, the method to be used are...Ch. 3.1 - In Exercises 33 to 36, the method to be used are...Ch. 3.1 - In quadrilateral ABCD, AC and BD are perpendicular...Ch. 3.1 - In ABC and DEF, you know that AD, CF, and ABDE....Ch. 3.1 - In Exercises 39 to 40, complete each proof. Given:...Ch. 3.1 - In Exercises 39 to 40, complete each proof. Given:...Ch. 3.1 - Given: ABC; RS is the perpendicular bisector of...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercises 1 to 4, state the reason SSS, SAS,...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 5 to 12, plan and write the two-column...Ch. 3.2 - In Exercise 13and 14, complete each proof. Given:...Ch. 3.2 - In Exercise 13and 14, complete each proof. Given:...Ch. 3.2 - Given: HJ bisects KHL HJKL See figure for exercise...Ch. 3.2 - Given: HJ bisects KHL HJKL In Exercise 15, you cam...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 17 to 20, first prove that triangles...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 21 to 26, ABC is a right triangle. Use...Ch. 3.2 - In Exercise 27 to 29, prove the indicated...Ch. 3.2 - In Exercise 27 to 29, prove the indicated...Ch. 3.2 - In Exercise 27 to 29, prove the indicated...Ch. 3.2 - In Exercise 30 to 32, draw the triangle that is to...Ch. 3.2 - In Exercises 30 to 32, draw the triangles that are...Ch. 3.2 - In Exercises 30 to 32, draw the triangles that are...Ch. 3.2 - Given: RW bisects SRU Prove: RSRU TRUVRS HINT:...Ch. 3.2 - Given: DBBC and CEDE Prove: ABAE BDCECD HINT:...Ch. 3.2 - In the roof truss shown, AB=8 and mHAF=37. Find: a...Ch. 3.2 - In the support system of the bridge shown, AC=6ft...Ch. 3.2 - As a car moves along the roadway in a mountain...Ch. 3.2 - Because of the construction along the road from A...Ch. 3.2 - Given: Regular pentagon ABCDE with diagonals BE...Ch. 3.2 - In the figure with regular pentagon ABCDE, do BE...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - For Exercises 1 to 8, use the accompanying...Ch. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - In Exercises 9 to 12, determine whether the sets...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - In Exercises 13 to 18, describe the line segments...Ch. 3.3 - Given that ABC is isosceles with ABAC, give the...Ch. 3.3 - Is it possible for a triangle to be: a an acute...Ch. 3.3 - A surveyor knows that a lot has the shape of an...Ch. 3.3 - In concave quadrilateral ABCD, the angle at A...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 23 to 28, use arithmetic or algebra,...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - In Exercises 29 to 32, suppose that BC is the base...Ch. 3.3 - Suppose that ABCDEF. Also, AX bisects CAB and DY...Ch. 3.3 - Suppose that ABCDEF. Also, AX is the median from A...Ch. 3.3 - In Exercises 35 and 36, complete each proof using...Ch. 3.3 - In Exercises 35 and 36, complete each proof using...Ch. 3.3 - In Exercises 37 to 39, complete each proof....Ch. 3.3 - In Exercises 37 to 39, complete each proof. Given:...Ch. 3.3 - In Exercises 37 to 39, complete each proof. Given:...Ch. 3.3 - In isosceles triangle BAT, ABAT.Also, BRBTAR, if...Ch. 3.3 - In BAT, BRBTAR, and mRBT=20. Find: a mT b mARB c...Ch. 3.3 - In PMN, PMPN, MB bisects PMN and NA bisects PNM....Ch. 3.3 - ABC lies in the structural support system of the...Ch. 3.3 - In Exercises 44 to 44, explain why each statement...Ch. 3.3 - In Exercises 46 to 48, explain why each statement...Ch. 3.3 - In Exercises 44 to 46, explain why each statement...Ch. 3.3 - Given: In the figure, XZYZ and Z is the midpoint...Ch. 3.3 - Given : In the figure, a=e=66. Also, YZZW. If...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 1 to 6, use line segments of given...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to 12, use, the angles provided to...Ch. 3.4 - In Exercises 7 to12, use the angle provided to...Ch. 3.4 - In Exercises 7 to 12, use, the angles provided to...Ch. 3.4 - In Exercises 13 and 14. use the angles and lengths...Ch. 3.4 - In Exercises 13 and 14. use the angles and lengths...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - In Exercises 15 and 18, construct angles having...Ch. 3.4 - Describe how you would construct an angle...Ch. 3.4 - Describe how you would construct an angle...Ch. 3.4 - Construct the complement of the acute angle Q...Ch. 3.4 - Construct the supplement of the obtuse angle T...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercises 23 to 26, use line segments of length...Ch. 3.4 - In Exercise 27 and 28, use the given angle R and...Ch. 3.4 - In Exercise 27 and 28, use the given angle R and...Ch. 3.4 - Complete the justification of the construction of...Ch. 3.4 - Given: AB with ACBCADBD by construction Prove:...Ch. 3.4 - To construct a regular hexagon, what measure would...Ch. 3.4 - To construct a regular octagon, what measure would...Ch. 3.4 - To construct a regular dodecagon 12 sides, what...Ch. 3.4 - Draw an acute triangle and construct the three...Ch. 3.4 - Draw an obtuse triangle and construct the three...Ch. 3.4 - Draw a right triangle and construct the angle...Ch. 3.4 - Draw an obtuse triangle and construct the three...Ch. 3.4 - Construct an equilateral triangle and its three...Ch. 3.4 - A carpenter has placed a square over an angle in...Ch. 3.4 - In right triangle ABC, mC=90. Also, BC=a, CA=b,...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - In Exercise 1 to 10, classify each statement as...Ch. 3.5 - Is it possible to draw a triangle whose angles...Ch. 3.5 - Is it possible to draw a triangle whose angles...Ch. 3.5 - Is it possible to draw a triangle whose sides...Ch. 3.5 - Is it possible to draw a triangle whose sides...Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - In Exercises 15 to 18, describe the triangle XYZ ,...Ch. 3.5 - Two of the sides of an isosceles triangle have...Ch. 3.5 - The sides of a right triangle have lengths of 6cm,...Ch. 3.5 - A triangle is both isosceles and acute. If one...Ch. 3.5 - One of the angles of an isosceles triangle...Ch. 3.5 - NASA in Huntsville, Alabama at point H, has called...Ch. 3.5 - A tornado has just struck a small Kansas community...Ch. 3.5 - In Exercises 25 and 26, complete each proof shown...Ch. 3.5 - In Exercises 25 and 26, complete each proof shown...Ch. 3.5 - In Exercises 27 and 28, construct proofs. Given:...Ch. 3.5 - In Exercises 27 and 28, construct proofs. Given:...Ch. 3.5 - For ABC and DEF not shown, suppose that ACDF, ABDE...Ch. 3.5 - In MNP not shown, point Q lies on NP so that MQ...Ch. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - In Exercises 31 to 34, apply a form of Theorem...Ch. 3.5 - Prove by the indirect method: Given: MPN is not...Ch. 3.5 - Prove by the indirect method: Given: Scalene XYZ...Ch. 3.5 - In Exercises 37 and 38, prove each theorem. The...Ch. 3.5 - In Exercises 37 and 38, prove each theorem. The...Ch. 3.CR - Given: AEBDEC AEDE Prove: AEBDECCh. 3.CR - Given: ABEFACDF12 Prove: BECh. 3.CR - Given: AD bisects BC ABBCDCBC Prove: AEDECh. 3.CR - Given: OAOB OC is the median to AB Prove: OCABCh. 3.CR - Given: ABDE ABDE ACDF Prove: BCFECh. 3.CR - Given: B is the midpoint of AC BDAC Prove: ADC is...Ch. 3.CR - Given: JMGM and GKJK GHHJ Prove: GMJKCh. 3.CR - Given: TNTRTONPTSPRTOTS Prove: NRCh. 3.CR - Given: YZ is the base of an isosceles triangle;...Ch. 3.CR - Given: ABDCABDC C is the midpoint of BE Prove:...Ch. 3.CR - Given: BADCDA ABCD Prove: AEDE HINT: Prove BADCDA...Ch. 3.CR - Given: BE is the altitude to AC AD is the altitude...Ch. 3.CR - Given: ABCDBADCDA Prove: AED is isosceles HINT:...Ch. 3.CR - Given: AC bisects BAD Prove: ADCDCh. 3.CR - In PQR not shown, mP=67 and mQ=23. a Name the...Ch. 3.CR - In ABC not shown, mA=40 and mB=65. List the sides...Ch. 3.CR - In PQR not shown, PQ=1.5, PR=2, and QR=2.5. List...Ch. 3.CR - Name the longest line segment shown in...Ch. 3.CR - Which of the following can be the lengths of the...Ch. 3.CR - Two sides of a triangle have lengths 15 and 20....Ch. 3.CR - Given:DBACADDCmC=70Find:mADBCh. 3.CR - Given: ABBCDACBCDmB=50 Find: mADCCh. 3.CR - Given: ABC is isosceles with base AB...Ch. 3.CR - Given: ABC with perimeter 40 AB=10BC=x+6AC=2x3...Ch. 3.CR - Given: ABC is isosceles with base AB...Ch. 3.CR - Given: AC and BC are the legs of isosceles ABC...Ch. 3.CR - Construct an angle that measures 75.Ch. 3.CR - Construct a right triangle that has acute angle A...Ch. 3.CR - Construct a second isosceles triangle in which the...Ch. 3.CT - It is given that ABCDEF triangles not shown a If...Ch. 3.CT - Consider XYZ triangles not shown a Which side is...Ch. 3.CT - State the reason SSS, SAS, ASA, AAS, or HL why The...Ch. 3.CT - Write the statement that is represented by the...Ch. 3.CT - With congruent parts marked, are the two triangles...Ch. 3.CT - With ABDCBE and A-D-E-C, does it necessarily...Ch. 3.CT - In ABC, mC=90 Find : a c if a=8 and b=6_ b b if...Ch. 3.CT - CM is the median for ABC from vertex C to side AB....Ch. 3.CT - In TUV, TVUV. Exercises 9, 10 a If mT=71, find mV....Ch. 3.CT - In TUV, TU. a If VT=7.6inches and TU=4.3inches,...Ch. 3.CT - Show all arcs in the following construction. a...Ch. 3.CT - Show all arcs in the following construction....Ch. 3.CT - In ABC, mC=46 and mB=93. a Name the shortest side...Ch. 3.CT - In TUV not shown, TUTVVU. Write a three-part...Ch. 3.CT - In the figure, A is the right angle,...Ch. 3.CT - Given ABC, draw the triangle that results when ABC...Ch. 3.CT - Complete all statements and reasons for the...Ch. 3.CT - Complete all missing statements and reasons in the...Ch. 3.CT - The perimeter of an isosceles triangle is 32cm. If...
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